A year ago Storck steered the Magyars to Euro 2016 in France, their first qualification for a major tournament since 1986.
"We are giving Bernd Storck another chance" said Sandor Csanyi head of the Hungarian Football Federation (MLSZ) in a statement after a marathon board meeting also attended by the German.
Last Friday's 1-0 away loss to tiny Andorra - ranked 186 in the world - ended Hungary's chances of qualifying for next year's World Cup tournament in Russia.
Pundits and fans at home rated the result as more embarrassing than a 2-1 loss to Malta in 2004, and 7-1 and 8-1 defeats to Yugoslavia and the Netherlands in 1997 and 2013 respectively.
A year ago Storck steered the Magyars to Euro 2016 in France, their first qualification for a major tournament since the 1986 World Cup.
Since then, Hungary has slumped to a string of defeats and also failed to beat another minnow the Faroe Islands.
Storck was appointed in 2015 to overhaul Hungary's youth structures, and took over from national team caretaker coach Pal Dardai later that year.
Previously a head coach with Kazakhstan, he is Hungary's second German coach after Lothar Matthaeus between 2004 and 2006.